1. Field of the Invention
The present invention relates to an apparatus and a method of generating membership functions for use in a fuzzy control operation employing predetermined fuzzy inference rules related to the membership functions, wherein a difference between a controlled variable attained from a control object and a target value, i.e. a control difference, is received as an input to conduct a fuzzy inference operation based on a predetermined fuzzy inference rule associated with the membership functions, and a manipulated variable resultantly obtained is supplied to the control object, thereby accomplishing a fuzzy control on the control object.
2. Description of Related Art
In a common practice, a PD (proportion and differentiation) control method has been used in this field. According to the PD control method, a manipulated variable u to be fed to a control object is defined as follows. EQU u=K.sub.p .multidot.e+K.sub.v .multidot.e (1)
where,
K.sub.p : Position gain PA1 K.sub.v : Velocity gain PA1 e: Position error PA1 e: Velocity error PA1 PM: Positive Medium. PA1 PS: Positive Small. PA1 ZR: Almost Zero. PA1 NS: Negative Small. PA1 NM: Negative Medium. PA1 PB: Positive Big. PA1 NB: Negative Big.
Let us assume here that the control object is represented as a linear lag (first-order lag) system and the target value to be supplied thereto is expressed as r. In this situation, the controlled value outputted as y (response characteristic) from the control object is represented by EQU y(s)=[K/(1+Ts)].multidot.r(s) (2)
where, s indicates a Laplace's operator or Laplacian.
In a region of time, Expression (2) is reduced to EQU y(t)=(i K/T).multidot.[exp(-t/T)].multidot.r(t) (3)
where, K stands for a gain constant and T denotes a time constant (to be utilized in the form of 1/T=.alpha. herebelow).
The position error e and the velocity error e is expressed as ##EQU1##
The expressions (4) and (5) indicate that the position error e and the velocity error e, namely, the response characteristic of the control object can be uniquely determined by the value of the gain constant K and the value of .alpha..
In this connection, FIG. 1 shows a response characteristic of a linear lag system. In the control operation, a gradient .alpha. (quickness) in the starting phase and an inclination .omega. (quickness of convergence) at a position where the output y takes a value in the vicinity (e.g. 80%) of the target value r serve primary roles.
FIG. 2 shows a graph of a phase plane in the PD control. The control operation is carried out such that a locus of a point is drawn from the initial point to follow a straight line of u=0 so as to reach the target point.
As described above and as can been seen from the graph of FIG. 1, the quickness in the starting phase and of the convergence in a linear lag system are determined depending on the values K and .alpha.. In addition, as shown in FIG. 2, according to the conventional PD control system, since the control operation is accomplished in the overall region of the phase plane based on the expression (1) and K.sub.p and K.sub.v are constant, the behavior of the control object is uniquely decided by the values K and .alpha. in the overall region, which disadvantageously leads to a problem of a minimized degree of freedom in the control operation.
When different control operations are desired to be achieved for respective regions according to the conventional PD control method, a plurality of PD control apparatuses are required to be disposed such that a change-over operation is appropriately conducted between these apparatuses depending on a state of the control object. This resultantly complicates the structure of the control apparatuses and hence increases the cost thereof.
On the other hand, a fuzzy control apparatus which has been recently highlighted and which has been increasingly put to practical uses is relatively simple in the configuration thereof and has an advantageous feature of developing arbitrary control characteristics. For example, depending on membership functions and fuzzy inference rules, a discontinuous control and a nonlinear control can be accomplished.
The fuzzy inference or reasoning rules represent knowledge, experiences, and know-how of experts of an objective control field and hence can be determined in a relatively easy manner.
However, in many cases, the contours and positions of the membership functions utilized in association with the fuzzy inference rules cannot be extracted from the knowledge of the experts. Moreover, there has not been defintely established a method of determining the membership functions. Heretofore, consequently, these functions are required to be obtained through a trial-and-error procedure.
FIG. 3 shows a membership function having a quite simple form i.e. a triangular shape. Also for a membership function having such a simple contour, it is necessary to determine a width (W.sub.L and W.sub.R and W.sub.L +W.sub.R), a height (H), and a center position (distance L from the origin O). A membership function needs be defined for each of the input/output variables and for each linguistic information or label (to be simply referred to as a label herebelow) related to each of the variables. In consequence, the total number of the membership functions is represented by a value which is attained by multiplying the number of the kinds of input and output variables by the number of the kinds of labels. For example, let us assume that the number of the labels and the number of the kinds of input variables are five and two, respectively. Under this condition, for the input variables (the antecedents of rules), ten (5.times.2) kinds of membership functions are required to be established.
FIG. 4a shows an example of typical membership functions. Each function is drawn in the form of an isosceles triangle of which a vertex has a grade of one. In this graph, adjacent triangles intersect each other at positions where the grade value is 0.5.
This graph includes five kinds of labels (or linguistic information) as follows.
In addition to the labels above, for example, the following labels may also be employed in relation to the membership functions, which will be described later.
FIG. 4b shows another example of membership functions each having a triangular shape.
Let us assume in this specification that for a triangle constituted with three points and three edges or sides therebetween, a point having a grade other than zero is called a vertex and each of two other points having a grade equal to zero is called an end point. Moreover, an edge between the vertex and an end point and an edge between the end points are to be called a hypotenuse or an oblique side and a base, respectively.
In the graph of FIG. 4b, all membership functions excepting one associated with the label ZR, namely, four membership functions respectively denoted with the labels PM, PS, NS, and NM each have an end point located at a center position.
In the cases respectively utilizing the membership functions of FIGS. 4a and 4b, even when the fuzzy control is accomplished depending on the same fuzzy rules, the behavior resulting from the control operation varies between the control objects respectively associated with the cases. Namely, the kinds and the contours of the membership functions may be arbitrarily changed and/or modified in various manners; moreover, the response characteristic of the control object alters depending on the kinds and the shapes of the membership functions. In consequence, it takes a considerably large amount of labor and a long period of time for the user to set and/or to adjust the membership functions in order to establish a desired control.